Recent content by andre220

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    Force on a point charge due to a sphere

    Is this method correct that I am using? Or should I use an image method here?
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    Force on a point charge due to a sphere

    Right, then I don't see how I can get the constants ##A_1, B_1## with only two boundary conditions. Thats why I only chose to keep ##l = 0## terms.
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    Force on a point charge due to a sphere

    Homework Statement An insulated conducting sphere of radius ##R##, carrying a total charge of ##Q##, is in the field of a point charge ##q## of the same sign. Assume ##q\ll Q##. Calculate and plot the force exerted by the sphere on ##q## as a function of distance from the center. In particular...
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    Potential anywhere inside a cube

    Okay, I take when ##x=0\implies## ##V_1##: ##A\sin{k_x 0} + B\cos{k_x 0} = V_1 \implies B = V_1## and I could keep going on like that for each of the six boundary conditions But I am still not seeing how that would work. Plus I don't see how I could get the ##k##'s from this.
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    Potential anywhere inside a cube

    Homework Statement All six faces of a cube, of side length ##L##, are maintained at constant, but different potentials. The left and right faces are at ##V_1## each. The top and bottom are at ##V_2## each. The front and back are at ##V_3##. Determine the electrostatic potential ##\Phi(x,y,z)##...
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    Alternative electrostatic potential

    In the case of a charge distribution I would integrate. So then I would just evaluate: $$ \Phi = \frac{1}{4\pi\epsilon_0}\int \frac{dQ}{r^{1+\delta}} $$ Inside we would have: $$\Phi(r<R) = \frac{1}{4\pi\epsilon_0}\int\limits_0^r \frac{dQ}{r^{1+\delta}}$$ and outside $$\Phi(r>R) =...
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    Alternative electrostatic potential

    Homework Statement Assume that the electrostatic potential of a point charge ##Q## is $$ \Phi(r) = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^{1+\delta}},$$ such that ##\delta \ll 1##. (a) Determine ##\Phi(r)## at any point inside and outside a spherical shell of radius ##R## with a uniform surface...
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    What is the force on an elementary dipole from a point charge in the same plane?

    Yes, thank you. It was quite simple once you pointed out the fact that ##F## should be a vector. And that ##p\cdot r = p r \cos{\theta}##. Thank you for your help.
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    What is the force on an elementary dipole from a point charge in the same plane?

    Homework Statement Show that the force on an elementary dipole of moment ##\mathbf{p}##, distance ##\mathbf{r}## from a point charge ##q## has components $$\begin{eqnarray} F_r &=& -\frac{qp\cos{\theta}}{2\pi\epsilon_0 r^3}\\ F_\theta &=& -\frac{qp\sin{\theta}}{4\pi\epsilon_0 r^3}...
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    Probability to overcome Coulomb repulsion

    Homework Statement The temperature in the interior of the Sun is about 1.5E7 K. Consider one of the reactions in the thermonulcear synthesis chain: p+p->H_2 + e^+ neutrino. In order for this reaction to occur two protons have to be at the distance of about 1 fm (10E-15 m). Estimate the...
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    Bohr Quantization with linear potential

    Thank you for your help. Got an answer of $$E_n = \alpha\left(\frac{3}{2}\frac{\pi\hbar}{\sqrt{2m}}(n+\frac{1}{2})\right)^{2/3}.$$ which seems okay.
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    Bohr Quantization with linear potential

    Right I see, so I get the two turning points at $$\pm \sqrt{\frac{E^2}{\alpha^2}}$$ and now its just a matter of evalutating the integral.
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    Bohr Quantization with linear potential

    Homework Statement Using Bohr's quantization rule find the energy levels for a particle in the potential: $$U(x) = \alpha\left|x\right|, \alpha > 0.$$ Homework Equations ##\oint p\, dx = 2\pi\hbar (n + \frac{1}{2})## The Attempt at a Solution Okay so: ##\begin{eqnarray} \oint p\, dx &= \int...
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    Is Particle 2 in the Eigenstate of ##S_z = \hbar/2##?

    So after some thought here is how I went about solving it: If particle one has ##S_x = -\hbar/2## then particle two must have ##S_x = \hbar/2## therefore the probability of measuring ##\hbar/2## for ##S_z## for particle two is: $$\left|\langle\chi^{(x)}_{+}|\chi^{(z)}_{+}\rangle\right|^2 =...
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    Is Particle 2 in the Eigenstate of ##S_z = \hbar/2##?

    The singlet state is: $$|00\rangle = \frac{1}{\sqrt{2}}(\uparrow\downarrow-\downarrow\uparrow)$$ As I understand it, the total spin that the two particles can carry is 0. So that would mean that if the first measurement is ##-\hbar/2## then the other must yield ##+\hbar/2## for the total spin to...
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